“…Around the shearless torus different nontwist phenomena were discovered in Hamiltonian systems, e.g., separatrix reconnections and island chains collisions [7], manifold reconnections of hyperbolic points in the chaotic regime [13], meandering [14], and the fractality of the shearless torus at criticality [8,15,16]. These phenomena were observed in area preserving maps [7,8,17] and Hamiltonian flows with one and a half [12,18] and two [19] degrees of freedom and they typically have a strong impact in transport properties of the system. In this paper we show the existence of the nontwist phenomena in time-reversible non-Hamiltonian maps and flows.…”